Thought Motor Theory Of



THREE-DOOR GAME SHOW PROBLEM/EFFECT. The controversy that surrounds the "correct answer" to the so-called three-door game show problem, also known as the Monty Hall problem/dilemma, is a noteworthy psychological phenomenon/effect in reasoning/decision-making (i.e., not all individuals can agree as to the "correct answer" to the problem even after simulating or reproducing the game for oneself). The probabilistic aspects underlying the three-door problem go back to Bertrand's box paradox, first described by the French mathematician Joseph L. F. Bertrand (1822-1900) in 1889, and later by the English-born American bridge expert Alan F. Truscott (1925- ) and the English author John Terrence Reese (1913-1996), according to which if a certain action could have been taken either because there was no alternative or as a result of a choice between two alternatives, then the first possibility is twice as likely as the second, other things being equal (also called the principle of restricted choice). In the most recent version of the three-door problem (cf., vos Savant, 1990), you are to imagine that you are on a game show, and you've been given a choice of three doors. Behind one door is a new car; behind each of the other two doors is a goat. You pick a door, say door No. 1, and the host - who knows what's behind the doors - opens another door, say door No. 3, which has a goat. The host then says to you, "Do you want to switch your choice and pick door No. 2?" The question/problem is the following: Is it to your advantage to switch your choice? (Remember, you have not yet seen what is behind door No. 1, your initial choice). The "correct answer" is "Yes, you should switch." The first door had a one-third chance of winning, but the second door now has a two-thirds chance. The following is offered as a good way to visualize the probabilistic dynamics involved in the three-door problem: Suppose (instead of just three doors) there are one-million doors, and you pick door No. 1. Then, the host (who knows what's behind the doors - and will always avoid the one with the prize) opens all the doors except door No. 333,333. Chances are, under these conditions, you would switch to that door without much hesitation. The "correct answer" to the three-door problem defines certain conditions, the most significant of which is that the host will always open a losing door on purpose (there's no way he can always open a losing door by chance). Anything else, theoretically, is a different question. In summary, for the three-door problem, when you first choose door No.1 from among the three doors, there is a one-third chance that the prize (new car) is behind that one and a two-thirds chance that it's behind the other doors. But, then, the host steps in and gives you a clue. If the prize is actually behind door No. 2, the host shows you door No. 3; and if the prize is actually behind door No. 3, the host shows you door No. 2. So, when you switch, you win if the prize is behind door No. 2 or door No. 3. You win either way. However, if you don't switch, you win only if the prize is behind door No. 1. See also PROBABILITY THEORY/LAWS. REFERENCES

Bertrand, J. L. F. (1889). Calcul des probabilities. Paris: Bossard. Reese, J. T. (1958/1973). The expert game.

New York: R. Hale. vos Savant, M. (1990). Three-door game show problem. Parade Magazine, December 2. (In Marilyn vos Savant's weekly column, "Ask Marilyn").

Brain Blaster

Brain Blaster

Have you ever been envious of people who seem to have no end of clever ideas, who are able to think quickly in any situation, or who seem to have flawless memories? Could it be that they're just born smarter or quicker than the rest of us? Or are there some secrets that they might know that we don't?

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